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Hyperconvex representations and exponential growth

Published online by Cambridge University Press:  25 January 2013

A. SAMBARINO*
Affiliation:
Département de Mathématiques, Université Paris Sud, F-91405 Orsay, France email andres.sambarino@gmail.com

Abstract

Let $G$ be a real algebraic semi-simple Lie group and $\Gamma $ be the fundamental group of a closed negatively curved manifold. In this article we study the limit cone, introduced by Benoist [Propriétés asymptotiques des groupes linéaires. Geom. Funct. Anal. 7(1) (1997), 1–47], and the growth indicator function, introduced by Quint [Divergence exponentielle des sous-groupes discrets en rang supérieur. Comment. Math. Helv. 77 (2002), 503–608], for a class of representations $\rho : \Gamma \rightarrow G$ admitting an equivariant map from $\partial \Gamma $ to the Furstenberg boundary of the symmetric space of $G, $ together with a transversality condition. We then study how these objects vary with the representation.

Type
Research Article
Copyright
©2013 Cambridge University Press 

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